I don't believe you need to re-invent the wheel system-wise. However, I would recommend against open-source rules.
The "" rules state no pre-creation of a system or pre-planning of text. Furthermore, I would add - it is supposed to be your complete RPG, not a supplement to something written by another.
Using a pre-made universal system like FUDGE, Myriad, Fuzion, or anything else meant as a toolkit, strikes me as bit too established for use as a base. These documents alone are longer than most 24 hour games. One day plus several weeks/months of work is outside the realm of this contest.
My call, is that you can borrow systems from your own projects or other 24 hour games - provided you change an element or two. (New attributes that work slightly differently, some differences in modifiers or combat means.)
Either way, honesty probably behooves you to type it again rather than cut and paste.
In short rewritten is ok, but prewriten is not.
As an aside, complete originality in game systems is a matter of degree. Supposedly US copyright law states you can't actually copyright a mechanic. (there are only so many ways to say "roll two six sided dice" after all) However, I'm no legal scholar so take this with a gain of salt.